All solutions of the equation x²+x+1 = yz in non-negative integers x,y,z are given in terms of an arithmetic continued fraction.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8, author = {A. Schinzel}, title = {On the diophantine equation x$^2$+x+1 = yz}, journal = {Colloquium Mathematicae}, volume = {139}, year = {2015}, pages = {243-248}, zbl = {06487241}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8} }
A. Schinzel. On the diophantine equation x²+x+1 = yz. Colloquium Mathematicae, Tome 139 (2015) pp. 243-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-8/